4225 — Dependent Transport Machine Preserves Route History
Claim
For the supplied circle HIT and univalent Boolean cover, the checked machine has explicit route syntax (variables, stay, turn, composition) and transport terms. Local reduction and evaluation are defined separately from interpretation. The formalization proves route/term substitution laws, reduction under substitution, closed progress, finite reduction traces for closed terms, preservation of actual circle-cover transport semantics, and execution/interpreter agreement. One turn changes the Boolean fiber from true to false at the same base index; two turns restore it. Retained source recovery is by reflexivity.
The semantic output-plus-correctness package is contractible for a fixed source, but route syntax and execution histories are not contracted. Endpoint-only actions and recovery of route syntax from Boolean output or the full Boolean action are refuted.
Scope
The operational result covers positive closed route words of the stated circle-cover machine, with its turn rule supplied and then proved sound. General dependent path syntax, inverse syntax, all-schedule termination, and integration with the separate Bool/Nat choose evaluator remain open; the identity generator is not claimed to generate nontrivial loop histories.
Subsequent proposal — 14 October 2026
Entry 4322 develops proof as sustained constructive capability, requiring recovery certificates to remain usable in subsequent interactions. The route-history distinctions proved here motivate its witness-sensitive continuation requirement. Its codimension-one sector count and candidate explanation of 1836 are additional proposed constructions, outside this machine's established scope.
Durable verification
Packet: research/nima/dependent-transport-machine.md; Agda source: research/nima/agda/DependentTransportMachine.agda; receipt: research/nima/results/dependent-transport-machine-formal-audit.json; SCC model: research/nima/scc-models/nima-dependent-transport-machine.json. Fresh safe closure, intended rejection, and source-bound SCC audit are reported as passing; not rerun for this entry.
Proposal ep_81c6123a-17e8-4f49-be36-1901c2227857, event ev-000000015693-5355af06-ec0d-4c3f-b3b7-70b0a05acf89. Sequence claim: seqclaim-2f7e5228c2a44f3c97613184 (entry 4225). Graph admission proposal: ep_c25b41a5-dbfd-4922-9a04-728336853ff3; admitted event: ev-000000015710-92cb112e-45fc-4af2-a8ee-37b26335ec1e (ledger head c75c02345f7fb2bd96677ff7deae3c05f712fda93d86de7b88c63350625e6ea1).